Measuring unit for synchronously collecting air dose rate and measurement position

Abstract

This paper describes a measuring unit for synchronously collecting the air dose rate and measurement position for efficient dosimetry surveying and data logging. The developed prototype comprises a three-dimensional light detection and ranging-based mapping part and dosimetry part, which are integrated into a single measuring unit through an embedded computer that installs a ROS (robot operating system) framework. The unit can function as a standalone system with embedded batteries. Since it is portable, on-line data gathering in the workspace can be realized, thereby maintaining consistency between the air dose rate and measurement position. In this paper, we describe the functional requirements for the measuring unit, the prototype system configuration, and the experimental results obtained in the mockup environment and nuclear facility to discuss its performance.

Introduction

The ongoing decommissioning of the Tokyo Electric Power Company Holdings Fukushima Daiichi Nuclear Power Station (Fukushima Daiichi NPS) is a challenging task that is termed as “Unknown unknowns”. It is important to minimize workers’ exposure to radiation and ensure their safety in an environment with unpredictable factors, including radiation. Some of the work is being conducted using remote control technology and systems such as robots for investigations, environmental preparation, and decontamination [1,2,3,4]. To conduct safe and steady work in the reactor building, the conditions of the workspace should be examined in advance, whenever possible, and a work plan should be drafted after a risk assessment. In particular, as radiation, mainly cesium-derived gamma rays, can affect workers and equipment, it is crucial to know their status. Radiation survey tasks are conducted regularly and continuously in parallel with other decommissioning tasks. There are two main methods for measuring gamma-derived radiation in the field. One method is to use a dosimeter, and the other is to use a gamma-ray imager. A dosimeter can directly measure air dose rates, although time and effort are required to determine the dose distribution in the target workspace. This is because measurements are performed by placing the dosimeter at a pointwise location to be measured. The method based on gamma-ray imagers is an effective confirmation method because it provides a visual presentation of high-dose areas by capturing the dose distribution. In fact, research and development activities include attempts to use a gamma-ray imager for measurements in the reactor building of the Fukushima Daiichi NPS [5] and to acquire three-dimensional (3D) radiation intensity distribution images using a gamma-ray imager mounted on a mobile robot [6]. However, gamma-ray imagers, in principle, visualize the relative radiation intensity within the angle of view and do not directly measure the air dose rate. In other words, a realistic way to determine the dose distribution in the target workspace is to interpolate or estimate the dose rates based on the air dose rate values measured at several points using dosimeters. Shi et al. [7] proposed a method for estimating the radiation source position based on discrete air dose rate data and measured positions using the Least Absolute Shrinkage and Selection Operator. Chao et al. [8] proposed a method for estimating the radiation distribution by the Maximum Likelihood Estimation from a plane source model calculated based on the count number in each grid by dividing the plane space into multiple grids; this method was more accurate than using a model calculated from measurements at representative points in each grid by simulation experiments. Simulation experiments showed that the proposed method is more accurate than a calculation model based on measurements at representative points in each grid. These works proposed computational dose distribution estimation methods using air dose rate, their measured positions, and discussed their effectiveness using computer simulations, however they did not mention practical methods to collect input data. Shinma et al. [9] reported a method for deriving gamma radiation dose distributions by ensemble averaging based on air dose rate data obtained from personal dosimeters worn by workers and robots moving within an operating plant, and the history of measurement positions was estimated using a head-mounted device. However, because it is assumed that workers wear the devices on their bodies and acquire data as they move, it is not always possible to acquire data at a desired point in the workspace. The dosimeter and position estimator are unintegrated as a unit and their relative pose in the setup for each measurement case must be considered.

In the field, the measured positions are recorded as the locations where the dosimeter is transported by workers or remotely operated equipment, using the vicinity of landmarks or characteristic structures placed in the workspace as a cue. The accuracy of the 3D position of the measurement points, as well as the air dose rate, as the input influences the accuracy of the calculation results; therefore, the position data must be recorded as accurately as possible. In particular, the limited accessible area at the decommissioning site of the Fukushima Daiichi NPS makes it necessary to estimate the dose distribution in workspaces where measurement is difficult from data collected in accessible areas. To improve the accuracy of the interpolation and estimation of the calculations, the 3D position data of the measurement points must be recorded together with the air dose rate data. Moreover, it is important for the design of the tool to be easily transportable and operable by workers, and to be able to acquire and record the air dose rate and measurement position in a short time.

Therefore, we designed and developed a measuring unit that synchronously collects 3D measurement position data during air dose rate data measurement in nuclear facilities. This paper describes the functional requirements for synchronous data collection and the measurement conditions, the prototype developed considering such requirements, and reports the measurement performance based on the results of data collection experiments conducted in a mockup field and at a nuclear facility.

Functional requirements

This section describes the functional requirements for synchronously collecting the air dose rate and measurement positions in the workspace. The target of the air dose rate measurement is gamma radiation.

In order to collect air dose rate data and 3D measurement position data together during a dose rate survey, the following functional requirements should be fulfilled.

• 1 Measurement of the air dose rate

• 2 Estimation of the 3D measurement position

• 3 On-line time-synchronized collection and recording both of 1 and 2

• 4 Standalone operation

To fulfill 1, the air dose rate of cesium-derived gamma radiation should be measured and recorded on computers and other devices. The sensors must meet the measurement specifications of the sensors used for air dose rate surveys at the Fukushima Daiichi NPS. To fulfill 2, because the target workspace in this study is indoor, methods that determine the position based on external signals, such as methods based on the Global Navigation Satellite System (GNSS), cannot be used. Therefore, the 3D air dose rate position must be estimated by setting the starting measurement position in the workspace online and estimating the relative 3D displacement from the set initial value based on the sensor data. For meeting 3, the data obtained by 1 and 2 in individual measurement and estimation cycles are stored in a time-matched format in a computer for later use. 4 is to ensure that 1 and 2 can be fulfilled to perform measurements without an external power supply. Furthermore, the functions should be integrated into a physically unified form to simplify manual transportation.

Hereinafter, a unit that fulfills these functional requirements is referred to as a “measuring unit”.

For radiation resistance, the effective dose for workers is defined as 50 mSv/year or 100 mSv/5 years, with radiation control at the level of a few mSv per task. According to the ref. [10], the radiation tolerance of commercial Central Processing Units and semiconductors is reported to be several tens of Gy (several tens of Sv in the case of gamma radiation). This means that the measuring unit can be configured using commercially available electronic components in the environment considered in this study where the operator can carry the measuring unit.

Measurement position estimation

The subject of this study is to develop a measuring unit that can measure air dose rate data while identifying its position. The following discussion deals only with the position of the air dose rate measurement, since measurements with the dosimeter involve data acquisition by holding the measurement point on the dosimeter over a desired point in the workspace. This section describes in more detail the requirement 2 for estimating the position of air dose rate measurement.

3D position estimation calculations

In order to estimate the 3D measurement position in an indoor environment where signals such as a GNSS, cannot be utilized, it is necessary to set the origin of the reference coordinate system in an arbitrary indoor space (hereinafter referred to as the spatial reference coordinate system), set the initial measurement pose (position and posture) in the spatial reference coordinate system, and estimate the relative amount of movement from the set initial position. Figure 1 shows the coordination systems. The estimated value ${}^L\Omega (t)$ of the air dose rate measurement point at time t in the spatial reference coordinate system $\{L\}$ can be written as follows.

$$\begin{aligned} {}^L\Omega (t) = ^LQ + \ ^L_{\Gamma }R \ ^{\Gamma }K(t) \in {{\textbf {R}}^{\textbf {3}}} \end{aligned}$$

(1)

where, $^LQ$ is the initial position vector of the representative position of the 3D pose estimator in the spatial reference coordinate system $\{L\}$. The $^L_{\Gamma }R$ on the right side of eq. (1) is a rotation matrix that indicates the orientation of the coordinate system $\{\Gamma \}$ that takes the initial orientation of the 3D pose estimator at time t in the spatial reference coordinate system $\{L\}$. Here, $^{\Gamma }K(t)$ is a position vector that indicates the relationship between the representative point of the 3D pose estimator $^{\Gamma }X(t)$ and the air dose rate measurement point in the coordinate system $\{\Gamma \}$ at time t. It is calculated by the following equation with position vector $^{\Gamma }X(t) \in {{\textbf {R}}^{\textbf {3}}}$ of the representative point of the 3D pose estimator on the coordinate system $\{\Gamma \}$ determined by the initial pose of the representative point of the 3D pose estimator with $^LQ$ as the origin, a rotation matrix $^{\Gamma }_{\Lambda }R(t)\in {{\textbf {R}}^{{\textbf {3}}\times {\textbf {3}}}}$, obtained from the pose of the 3D pose estimator and a vector $^{\Lambda }\kappa \in {{\textbf {R}}^{\textbf {3}}}$ that indicates the offset vector of the positions of the air dose rate measurement point in the coordinate system $\{\Lambda \}$ with the origin at the representative point of the 3D pose estimator $^{\Gamma }X(t)$.

$$\begin{aligned} ^{\Gamma }K(t) = ^{\Gamma }X(t) + \ ^{\Gamma }_{\Lambda }R(t) \ ^{\Lambda }\kappa \end{aligned}$$

(2)

Here, eq. (1) can be rewritten as follows.

$$\begin{aligned} ^L\Omega (t) = ^LQ + \ ^L_{\Gamma }R \left( \ ^{\Gamma }X(t) \ + \ ^{\Gamma }_{\Lambda }R(t)\ ^{\Lambda }\kappa \right) \end{aligned}$$

(3)

Furthermore, considering $^LQ$ and $^L_\Gamma R$, a method is required to identify the initial posture of the 3D posture estimator in the spatial reference coordinate system $\{L\}$ based on the sensor data mounted on the measuring unit. Specifically, $^LQ$ and $^L_{\Gamma }R$ need to be set by adding certain conditions to the measurement procedure.

Initial pose setting

Here, we describe how to set $^LQ$ and $^L_{\Gamma }R$. The target workspace in this study is an indoor environment where GNSS-based methods cannot be used. In addition, it is difficult to deploy and install external position-measuring equipment. In addition, measurement work in the field is conducted by an unspecified number of workers. Therefore, it is necessary to adopt a method that allows workers to set the initial pose of the measuring unit without using any special measuring equipment. Here, we consider setting the spatial reference coordinate system $\{L\}$ with the z-axis vertically upward on an arbitrary horizontal floor surface and, aligning the x and y axes of the representative point of the 3D pose estimator with the origin of $\{L\}$ on the floor surface, and align the posture of $\{L\}$ with the initial posture of the 3D pose estimator (initial posture of the coordinate system $\{\Gamma \}$). Thus, only the height direction (z value) of the initial position of the representative point of the 3D pose estimator is indeterminate. In the field, it is feasible to measure the initial height by setting the representative point of the 3D pose estimator above the origin of the coordinate system on the floor of the workspace. The following data are then obtained by measuring the initial height of the 3D pose estimator h.

$$\begin{aligned} ^LQ= & {} \begin{bmatrix} 0\\ 0\\ h\\ \end{bmatrix} \in {{\textbf {R}}^{\textbf {3}}} \end{aligned}$$

(4)

$$\begin{aligned} ^L_{\Gamma } R= & {} \begin{bmatrix} 1 &{} 0 &{} 0 \\ 0 &{} 1 &{} 0 \\ 0 &{} 0 &{} 1 \\ \end{bmatrix} \in {{\textbf {R}}^{{\textbf {3}}\times {\textbf {3}}}} \end{aligned}$$

(5)

In other words, by measuring the initial height of the representative point of the 3D pose estimator at the initial posture setting, it is possible to obtain the estimated value $^L\Omega (t)$ of the measurement point on the dosimeter. Although errors will occur depending on the initial posture and position, the proposed method is realistic from the viewpoint of on-site operation because it allows the initial pose setting in a short time. Here, the origins of $\{L\}$ and $\{\Gamma \}$ can be perfectly matched as $^LQ=[0, 0, 0]^T$ for the spatial reference coordinate system. In this case, the representative point of 3D pose estimator must be grounded; however this condition is not appropriate in terms of equipment contamination given, the assumed workspace in this study.

Prototype of measuring unit

This section describes the prototype measuring unit, which was constructed by selecting sensors and designing the system as a unit based on the functional requirements and initial conditions. Figure 2 shows the appearance of the developed measuring unit, and Fig. 3 shows the system configuration. A Raspberry Pi 4 was used as the computer for integrated data acquisition and recording, and a Polimaster BDG2 gamma radiation detection sensor (Geiger-Mueller tube gamma radiation sensor, measurement range: 0.1 $\mu$Sv/h –10 Sv/h and sensitivity: 45 cpm/($\mu$Sv/h)) was adopted as the dosimeter for measuring the gamma radiation air dose rate to satisfy requirement 1. In addition, a compact 3D mapping unit Stencil2-16 [11] (Kaarta Inc.) that can calculate pose estimation in real time was used as a 3D pose estimator. The proposed method provides data to calculate relative movements among the instruments used for meeting requirement 2. Stencil2-16 can calculate 3D pose estimates from point cloud data measured by a 3D-LiDAR data from an Inertial Measurement Unit (IMU), and captured camera images. BDG2 is connected via a Universal Serial Bus (USB), and Stencil2-16 is connected via Ethernet to a computer (Raspberry Pi 4) for integrated data acquisition and recording. To satisfy the requirement 2, a TeraRanger Evo3m (range: 0.1–3.0 m and output resolution: 0.005 m) [12] manufactured by Terabee was installed at the bottom part of the measuring unit to measure the height of the representative point of the measuring unit when starting the measurement. This step is necessary when initial position setting method is applied. The TeraRanger Evo3m is connected to Raspberry Pi 4 via USB. In addition, to satisfy the requirement 4, one 19 V battery for the Stencil2-16 and a 5 V battery for the computer are incorporated; thus, independent operation of the measuring unit is achieved.

These are the main hardware components of the measuring unit.

To realize a software configuration that satisfies requirement 3, we use the Robot Operating System (ROS) [13], a metaoperating system for developing robot systems, etc., as the software infrastructure for implementing and systemizing the data measurement and collection functions. Stencil2-16 has a built-in computer with an ROS (Kinetic Kame) installed that can output the calculation results of the position estimation as a standard. The ROS network is configured with Stencil2-16 set as the ROS master, and Raspberry Pi 4, a computer used for integrated data acquisition and recording, with Ubuntu 18.04 LTS and ROS (Melodic Morenia) are connected to the ROS master via a TCP/IP network. The publisher application is executed on a Raspberry Pi 4 computer and reads data from BDG2 at regular intervals (1 Hz) and provides these data to the ROS network. In parallel, by running another program developed in Raspberry Pi 4, the air dose rate measurement position are calculated using the estimated position data output from Stencil2-16 and are published on the ROS network at regular intervals (200 Hz). In addition, a program is executed to subscribe to the above data and publish the integrated data in a time-aligned format at regular intervals (200 Hz). The data published in a time-aligned format at regular intervals (1 Hz) are recorded in the bag file format, which is the standard data recording format in ROS. The recorded data are stored in a storage device (a micro SD card) inserted in the Raspberry Pi4 computer. To measure the initial height of the representative point of the measuring unit, an ROS program that publishes distance data from a TeraRanger Evo3m is run in parallel. Figure 4 shows such data flow in a measuring unit.

Thus, a measuring unit was designed, and a prototype was constructed to satisfy the functional requirements.

Furthermore, to practically integrate and collect the air dose rate and measurement position with the setup, the following points should be considered.

The initial height of the representative point of the measuring unit must be estimated by satisfying the initial conditions before measurement initiation and by acquiring data using a distance sensor. Because noise is assumed to arise in the height-measurement phase, we consider implementing multiple distance measurements to check the data variance and calculate the average value. Figure 5 indicates a side view of the prototype of the measuring unit. The height of the representative point of the 3D pose estimator from the floor and the height offset $\delta$ to the height of the dose rate measurement point from the height of the representative point of 3D pose estimator. This height offset is used to calculate the measurement position at time t, it is described separately for ease of description in later explanation. The following procedure is used to derive the initial height of 3D pose estimator $\mu$ and the initial height of the measurement position $h+\delta$.

• (i) Derive the variance value $\sigma$ by following equation, when $\mu$ is the mean value of N samples of the height of the representative point of 3D pose estimator(the origin of $\{\Lambda \}$) $h_i$ derived by referring to the distance measurement with the initial pose.

  $$\begin{aligned} \mu = \frac{1}{N} \sum _{i=1}^{N} h_i \end{aligned}$$

  (6)
  $$\begin{aligned} \sigma ^2 = \frac{1}{N} \sum _{i=1}^{N} (h_i - \mu )^2 \end{aligned}$$

  (7)

• (ii) Perform the threshold processing for $\sigma$.

  • If $\sigma$ is greater than the threshold, return to (i) and the height data is measured.

  • If $\sigma$ is less than the threshold value, then calculate the initial height of 3D pose estimator $h=\mu$ and the initial height of measurement position is derived as $h+\delta$ considering the height offset $\delta$ between the measurement point on the dosimeter and the representative point of measuring unit.

In this study, in the developed prototype, the height offset $\delta$, sampling number N, and threshold of $\sigma$ are set to 0.239[m], 500, and 0.01, respectively. The value of $\sigma$ was set with the intention of maintaining variation within 0.01 m because it is desirable for the pose to remain constant during the initial pose setting.

Here, we describe synchronous data acquisition. The cycles of 3D pose estimation calculation and spatial dose rate data acquisition are 200 Hz and 1 Hz, respectively (Fig. 4). For this reason, synchronous data collection is implemented by acquiring data from the latest 3D pose estimation calculation results using the timing of the spatial dose rate data acquisition at 1 Hz as a trigger. Finally, the data is published at 1 Hz in the form of ${\textbf {R}}^5$ floating-point array data consisting of the spatial dose rate data acquisition time, the 3D estimated position, and the spatial dose rate and saved in a file. Data Integration in Fig. 4 is the part for data synchronization. This process is implemented using the ROS framework, and published data are saved in a rosbag file.

By setting the initial pose, $^L\Omega (t)$ is calculated by the following equation under the conditions specified by eqs. (4) and (5).

$$\begin{aligned} ^L\Omega (t) = \begin{bmatrix} 0\\ 0\\ h \end{bmatrix} + ^{\Gamma }X(t) + ^{\Gamma }_{\Lambda }R(t) \ ^{\Lambda }\kappa \end{aligned}$$

(8)

where $^{\Lambda }\kappa =[0,0,\delta ]=[0,0,0.239]^T$ from the structure of the prototype of measuring unit.

Here, we describe the posture of the 3D pose estimator for the coordinate system $\{\Gamma \}$ obtained at time t as the quaternion $q(t)=q_0(t)+q_1(t){\textbf {i}}+q_2(t){\textbf {j}}+q_3(t){\textbf {k}}$ with quaternion coefficients $(q_0(t), q_1(t), q_2(t), q_3(t))$. The quaternion is adopted here because it represents a smooth attitude shift without singularities. Therefore, the rotation matrix $^{\Gamma }_{\Lambda } R(t)$ is defined as follows.

$$\begin{aligned} ^{\Gamma }_{\Lambda } R(t)= & {} \begin{bmatrix} ^{\Gamma }_{\Lambda }r_{11}(t) &{} ^{\Gamma }_{\Lambda }r_{12}(t) &{} ^{\Gamma }_{\Lambda }r_{13}(t) \\ ^{\Gamma }_{\Lambda }r_{21}(t) &{} ^{\Gamma }_{\Lambda }r_{22}(t) &{} ^{\Gamma }_{\Lambda }r_{23}(t) \\ ^{\Gamma }_{\Lambda }r_{31}(t) &{} ^{\Gamma }_{\Lambda }r_{32}(t) &{} ^{\Gamma }_{\Lambda }r_{33}(t) \\ \end{bmatrix} \in {{\textbf {R}}^{{\textbf {3}}\times {\textbf {3}}}}\end{aligned}$$

(9)

$$\begin{aligned} ^{\Gamma }_{\Lambda }r_{11}(t)= & {} q_0^2(t)+q_1^2(t)-q_2^2(t) -q_3^2(t) \end{aligned}$$

(10)

$$\begin{aligned} ^{\Gamma }_{\Lambda }r_{12}(t)= & {} 2( q_1(t)q_2(t)-q_0(t)q_3(t)) \end{aligned}$$

(11)

$$\begin{aligned} ^{\Gamma }_{\Lambda }r_{13}(t)= & {} 2( q_1(t)q_3(t) +q_0(t)q_2(t)) \end{aligned}$$

(12)

$$\begin{aligned} ^{\Gamma }_{\Lambda }r_{21}(t)= & {} 2( q_1(t)q_2(t)+q_0(t)q_3(t)) \end{aligned}$$

(13)

$$\begin{aligned} ^{\Gamma }_{\Lambda }r_{22}(t)= & {} q_0^2(t)-q_1^2(t)+q_2^2(t) -q_3^2(t)\end{aligned}$$

(14)

$$\begin{aligned} ^{\Gamma }_{\Lambda }r_{23}(t)= & {} 2( q_2(t)q_3(t) -q_0(t)q_1(t)) \end{aligned}$$

(15)

$$\begin{aligned} ^{\Gamma }_{\Lambda }r_{31}(t)= & {} 2( q_1(t)q_3(t) -q_0(t)q_2(t)) \end{aligned}$$

(16)

$$\begin{aligned} ^{\Gamma }_{\Lambda }r_{32}(t)= & {} 2( q_2(t)q_3(t) +q_0(t)q_1(t)) \end{aligned}$$

(17)

$$\begin{aligned} ^{\Gamma }_{\Lambda }r_{33}(t)= & {} q_0^2(t)-q_1^2(t)-q_2^2(t) +q_3^2(t) \end{aligned}$$

(18)

The measurement point on the dosimeter in the coordinate system $\{\Lambda \}$ is at a vertical distance of 0.239 m from the origin of the coordinate system $\{\Lambda \}$. Therefore, since $^\Lambda \kappa =[0, 0, 0.239]^T$, the position $^L\Omega (t)$ of the air dose rate measurement position from the origin of the 3D pose estimator at time t can be rewritten as follows.

$$\begin{aligned} ^L\Omega (t) = \begin{bmatrix} 0\\ 0\\ h \end{bmatrix} + ^{\Gamma }X(t)+ \begin{bmatrix} 0.239 \ ^{\Gamma }_{\Lambda }r_{13}(t) \\ 0.239 \ ^{\Gamma }_{\Lambda }r_{23}(t) \\ 0.239 \ ^{\Gamma }_{\Lambda }r_{33}(t) \end{bmatrix} \end{aligned}$$

(19)

In this case, the initial values are obtained from the conditions $^{\Gamma }X(0)=[0,0,0]^T, ^{\Gamma }_{\Lambda }r_{13}(0)=0, ^{\Gamma }_{\Lambda }r_{23}(0)=0$ and $^{\Gamma }_{\Lambda }r_{33}(0)=1$. These conditions are obtained by setting the initial pose.

$$\begin{aligned} ^L\Omega (0) = \begin{bmatrix} 0\\ 0\\ h + 0.239 \end{bmatrix} \end{aligned}$$

(20)

Experiments to verify performance of prototype

We conducted experiments to verify the operation of the estimation of the air dose rate measurement position using the prototype of the measuring unit. The purpose of the experiments is to demonstrate and confirm practical performance in the workspaces with the characteristics of a nuclear facility.

First, to verify the position estimation of the prototype, experiments were conducted in a simulated plant-like mockup field installed in the test building of the Naraha Center for Remote Control Technology Development of the Japan Atomic Energy Agency (NARREC) [14, 15]. Figure 6 shows the appearance of the simulated plant mockup field ($10 \times 10 \textrm{m}$) used in the experiment and the experimental conditions. The mockup field was constructed in the area where the motion capture system [16] (with 16 Vicon T20S cameras) was installed in the NARREC test building. In the experiments, the position estimation performance was verified by comparing the positions measured by motion capture with those estimated by the developed prototype. To move the measuring unit from the origin of the coordinate system, a camera setting pole was connected under the measuring unit, and the operator moved the measuring unit by handling it. The operator is instructed to move the measurement point on the dosimeter as close as possible to the target location, stand still for a while, and then move around several target locations in the specified order.

In Fig. 7, figures of the spatial model generated by the high-precision 3D laser scanner FARO Focus Laser Scanner S350 are superimposed [17]. The spatial reference coordinate system $\{L\}$ at the time of the experiment is indicated by symbols (red: x-axis, green: y-axis, blue: z-axis) indicating the coordinate system near the entrance to the simulated plant environment in the rightmost area of each figure in Fig. 7. Experiments were conducted in this spatial reference coordinate system using the initial pose setting, and the measurement position was estimated by moving the measuring unit to predetermined points. The average of quaternion coefficients of the posture of the measuring unit from the initial setup to the start of measurement in Experimet1 and Experinemt2 of NARREC were (0.999712971, 0.007880682, $-$0.021865909, $-$0.005712253) and (0.999784816, 0.001587495, $-$0.020475754, $-$0.002504513), respectively. Here, the quaternion coefficients are (1.0, 0.0, 0.0, 0.0) when the measuring unit is in the upright pose. In this case, target locations are presented as markers in the air, and the order in which to move around the predetermined target locations. The magenta dots in Fig. 7 indicate the position estimation results obtained using the developed measuring unit, and the dark blue dots indicate the positions measured by motion capture (i.e., positions of measurement points on the dosimeter calculated using multiple markers tracked at 100 Hz). Figure 8 shows the errors in the position, where the maximum error was approximately 0.25 m. Here, the number of data samples at target locations from N1 to N8 in Experiment 1 at NARREC were 14, 27, 24, 22, 26, 18, 24, and 27. The number of data samples at target locations from N1 to N8 in Experiment 2 at NARREC were 20, 21, 23, 30, 29, 20, 24, and 31.

Measurement experiments were conducted in the pool canal circulating system room of the Japan Materials Testing Reactor of the Japan Atomic Energy Agency (JMTR) [18] to verify the synchronous collection of position and dose rate data in nuclear facilities. Because decommissioning of the JMTR had already been decided and its operation had been terminated in preparation for decommissioning, we consider that the JMTR is a suitable experimental environment for verification. This occurs because the radiation level is sufficiently low to allow workers to access the facility. In this experiment, a 1.4 m-long camera-setting pole was connected to the measuring unit, and its initial pose was set with the lower end of the pole supporting the measuring unit grounded at the origin of the environment. Because it was difficult to deploy and set up the motion capture system in the pool canal circulating system room of the JMTR, we decided to use the ground truth of the measurement position as the value obtained by attaching a camera setting pole to the developed measuring unit and standing vertically on a mark placed on the floor surface in advance. The experimental conditions at JMTR were the same as those at NARREC, except for the holding of the measuring unit over the target locations. Figures 9 and 10 show the plots of the positions estimated by the measuring unit and the results of the position error at each location. Here, the average of quaternion coefficients of the posture of the measuring unit from the initial setup to the start of measurement in Experimet1 and Experinemt2 of JMTR were (0.999889267, $-$0.002511705, $-$0.012693517, 0.003417743) and (0.999795354, 0.000734641, $-$0.017163065, $-$0.00403325), respectively. This result indicates that the maximum position error was approximately 0.4 m. Here, the number of data samples at the target locations from J1 to J9 in Experiment 1 at JMTR are 19, 19, 21, 23, 28, 20, 21, 21, 25. The number of data samples at the target locations from J1 to J8 in Experiment 2 at the JMTR are 32, 33, 31, 34, 28, 23, 31, 29, and 24. Compared to J1, J2, J3, J4 and J9 on Fig. 9, the space around J5, J6, J7 and J8 was narrower (within a radius of approximately 1 m), which was less than the minimum measurable distance of 1 m for the 3D mapping unit. Thus, the position estimation calculation may not be fully functional.

Tables 1 and 2 indicate the air dose rates obtained from the measuring unit at each position during the experiments. The values were measured separately at each point by Techno AP TC200 (range: 0.001–20$\upmu$Sv/h, sensitivity: 15,000 cpm/($\upmu$Sv/h)), a measuring instrument with higher sensitivity than the dosimeter in the developed measuring unit, and were used as the ground truth. The minimum, median, and maximum values are shown after the data had stabilized (defined as 15sec after the measuring unit was moved to each point). Although the magnitude of the error varied from site to site in each result, an overall potential trend was observed. This trend may be attributed to the relatively low doses. The tolerances of the BDG2 are ±20.25$\%$ at 8$\upmu$Sv/h and ±22.5$\%$ at 0.8$\upmu$Sv/h. Compared with the ground-truth data, the measured values by measuring unit are generally within this range. Considering that air dose rates fluctuate even at the same location, the results do not significantly deviate from the true values and are considered reasonable.

It is considered that the results obtained in this study present realistic data that would be obtained at a nuclear facility to the radiation distribution estimation method based on discretely measured data such as cited in the Introduction. We expect that the results obtained will contribute to the consideration of research and development of methods for robust radiation distribution estimation.

Application

The developed measuring unit can also be mounted on an object-carrying platform, such as a mobile robot, to perform measurement tasks because of its portability and independent operation ability. The unit can be easily mounted on a mobile robot platform using jigs, bolts, and attachments. Figure 11 depicts a setup in which the measuring unit is mounted on a mobile robot to perform continuous measurements after being transported by a person. Thus, this measuring unit can be used to seamlessly acquire data across workspaces where workers can operate and areas that are inaccessible to workers. Figure 12 shows the trajectories of the measuring unit recorded during the demonstration, which are shown in Fig. 11. Such retrofit characteristics make it possible to measure the air dose rate simultaneously while measuring the position without major modifications to the existing equipment. This achievement is expected to contribute to the expansion of the target workspace.

Conclusion

This paper describes a measuring unit for the synchronous collection of air dose rates and measurement positions at nuclear facilities. The requirements for such synchronous collection are summarized. A prototype of measuring unit that satisfies the requirements was constructed by integrating a dosimeter, a 3D mapping unit, a distance sensor, and an embedded computer and tested. In addition, the position and initial pose estimation methods were integrated. The results of experiments in an experimental environment simulating a nuclear facility and in an actual nuclear facility are reported in this paper.

In future, we plan to consider the use of data collected by the measuring unit along with the 3D environmental model data based on the spatial structure identification method [19, 20]. The proposed structure identification method is currently under development for use in dose distribution estimation calculations and other applications. We also intend to improve the radiation resistance by shielding the developed measuring unit.

Fig. 1

Coordinate frames

Fig. 2

Appearance of the prototype of measuring unit

Fig. 3

System configuration

Fig. 4

Data flow in measuring unit

Fig. 5

Height definition at initial pose setting

Fig. 6

A snapshot of the experiment

Fig. 7

Experimental results in mockup field in NARREC

Fig. 8

Position estimation error in experiments at NARREC

Fig. 9

Experimental results in pool canal room of JMTR

Fig. 10

Position Estimation Error in Experiments at JMTR

Fig. 11

Demonstration of handing over measuring unit from person to mobile robot

Fig. 12

Recorded trajectory of demonstration

Table 1 Measured dose rate of experiment1 at JMTR

Table 2 Measured dose rate of experiment2 at JMTR